SOLUTION: The amount of money that a local charity earns by selling T-shirts at a mall depends on the price of each T-shirt. The monthly profit,y, in dollars is given by the quadratic equat

Question 1183301: The amount of money that a local charity earns by selling T-shirts at a mall
depends on the price of each T-shirt. The monthly profit,y, in dollars is given by the quadratic equation y=-35x^2 + 1250x - 6500 where,x,represents the price of each T-shirt.
d) Under what circumstances will the charity maximize its profit (make the most money)?
e) Describe the significance of the roots in terms of the graph and in terms of the charity’s venture
f) Determine the range of prices that the charity could consider, in order to
make a monthly profit of at least $3000. Thanks for the help
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The maximum is where x=-b/2a=-1250/-70=$17.86 and will make $4660.71 in profit. That is the price at which profit is maximized.
The roots represent where the profit is 0 or breakeven.
Set y=3000 and solve for -35x^2+1250x-9500=0
or 35x^2-1250x+9500=0; 7x^2-250x+1900=0
x=(1/14)* (250+/- sqrt (9300))
=(1/14)(250+/- 96.44)
=$24.74 or $10.98
between ($10.98 and $24.74)

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